Theoretical model and experimental analysis of a high pressure PEM water electrolyser for hydrogen production

international journal of hydrogen energy 34 (2009) 1143–1158

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Theoretical model and experimental analysis of a high pressure PEM water electrolyser for hydrogen production F. Marangio*, M. Santarelli, M. Calı` Dipartimento di Energetica, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy

article info

abstract

Article history:

This work aims at analysing the performances of a prototype of a high pressure Polymer

Received 24 July 2008

Electrolyte Membrane water electrolyser.

Received in revised form

The whole work was funded in the framework of the Italian FISR (Research special

19 November 2008

supplementary funding) project. The high pressure electrolyser prototype was manufac-

Accepted 29 November 2008

tured by Giner Inc. (Massachusetts, USA), whereas the test bench was expressly designed

Available online 4 January 2009

and built thanks to the collaboration with LAQ INTESE (High Quality Laboratory – Technological Innovation for Energetic Sustainability) and with Sapio SpA (Monza, Milan, Italy).

Keywords:

An electrochemical model of the electrolyser stack is developed, which calculates the

Hydrogen production

theoretical open-circuit voltage via a thermodynamic analysis of the process, and then

High pressure water electrolysis

obtains the expected real voltage during operation by calculating the different overvoltages

Modelling

as function of the current. The final result of the model is a theoretical polarisation curve.

Experimental

Experimental results are then presented and compared with the model theoretical results, and thanks to an experimental data fitting it is possible to obtain the estimated values of some important process parameters and their trend in different temperature and pressure conditions. ª 2008 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.

1.

Introduction

The manufacturing of hydrogen via high pressure electrolysis is a technology with high potential of further development. In fact, it can bring huge cost reduction and plant simplification by avoiding the need for a subsequent hydrogen compression. Moreover, according to many authors [10,11], the power required to produce hydrogen via atmospheric electrolysis with subsequent compression is higher than that required by high pressure electrolysis: thus the use of the latter could bring an efficiency improvement in the hydrogen production process via water electrolysis. Other authors report in the International Journal of Hydrogen Energy [1] that they think

atmospheric electrolysis to be preferable, though their analysis mainly focuses on alkaline electrolysis rather than PEM electrolysis. In the framework of the Italian FISR (Research special supplementary funding) project, a prototype of high pressure PEM electrolyser has been tested. Peculiarity of the prototype is the unbalanced pressure across the membrane: in fact the anodic chambers are at almost atmospheric pressure, whereas the cathodic chambers are at pressure up to 7 MPa. This causes the membrane to be mechanically stressed, but also eliminates the need for bringing water at high pressure, thus allowing further energy saving and reducing the complexity of the Balance of Plant (BOP).

* Corresponding author. Tel.: þ39 011 564 4487; fax: þ39 011 564 4499. E-mail address: [email protected] (F. Marangio). 0360-3199/$ – see front matter ª 2008 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2008.11.083

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List of symbols Latin letters C concentration, mol/m3 D diffusion coefficient, m2/s E cell reversible potential, V G molar Gibbs free energy, J/mol H molar enthalpy, J/mol h height, mm I cell current, A i cell current density, A/m2 i0 exchange current density, A/cm2 j counting index, – L rectangular MEA length, m average length, m Lavg [ generic length, m M molar mass, g/mol n number of channels, – N_ molar flow, mol/s n_ net water molar flow per area unit, mol/(s m2) _ NH O;m net water molar flow through the membrane, mol/s 2

P p P0 Qp R R S S_ gen T t T0 V w Wel Wrev y z

total pressure, MPa partial pressure, MPa standard pressure, MPa reaction quotient, – (with subscript) resistance, ohm (without subscript) universal constant of gases, J/(mol K) molar entropy, J/(mol K) rate of entropy generation, J/(mol K s) temperature, K time, s standard temperature, K cell voltage, V width, mm electrical work, J work in reversible conditions, J molar fraction, – number of electrons transferred during the reaction, –

Greek letters F heat flow, W J work flow, W work flow in reversible conditions, W Jrev r resistivity, ohm m Nafion membrane conductivity, S/m sm a transfer coefficient, – d thickness, mm DG molar Gibbs free energy variation during the reaction in any condition, J/mol DH enthalpy variation during the reaction, J/mol DS entropy variation during the reaction, J/(mol K)

Aims of this paper are to show the theoretical model, which has been developed in order to describe the polarisation curve of the electrolyser, and to present the results of the experiments carried on to validate the model.

Subscripts hydrogen ions Hþ hydrogen H2 water H2O oxygen O2 act activation an anode c channel (with w, h), critical (with T, P) c critical cat cathode cell cell ch in the channels cons consumed dd diffusion diff diffusion e electrode eff effective eo electro-osmotic drag eq equivalent f formation g gaseous in inlet flow l liquid m membrane mem membrane me at the membrane–electrode interface ohm ohmic out outlet flow pe pressure effect pl plate prod produced s channel support w water Superscripts 0 in standard conditions * standard pressure and generic temperature Constants A MEA area, 160 cm2 CHþ concentration of hydrogen ions in the membrane, 1000 mol/m3 Dw water diffusion coefficient through the membrane, 1.28  1010 m2/s e electron charge, 1.6  1019 C F Faraday constant, 96485 C/mol membrane permeability to water, 1.58  1018 m2 Kdarcy Ke membrane electric permeability, 1.13  1019 m2 Na Avogadro number, 6.022  1023 1/mol electro-osmotic drag coefficient, 7 molH2 O =molHþ nd 3 electrodes porosity, 0.3 electrodes percolation threshold, 0.11 3p water density, 1000 kg/m3 rH2 O mH 2 O water viscosity, 1.1  103 Pa s

2.

Literature analysis

High pressure PEM electrolysis is a quite recent research field, and therefore the scientific literature is quite scarce. On the

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international journal of hydrogen energy 34 (2009) 1143–1158

contrary literature about PEM fuel cells is very abundant and often useful since PEM electrolysers share many issues with PEM fuel cells. Onda et al. [10] conduct an analysis of the electrical power needed to produce hydrogen at high pressure by water electrolysis. Both the cases of atmospheric electrolysis with subsequent compression and high pressure electrolysis are taken into consideration. Production power is estimated with the Nernst equation, considering enthalpy and entropy change both with temperature and pressure. The results of the proposed model show that at 70 MPa power savings up to 6% can be achieved through high pressure electrolysis. However, just the ideal open-circuit voltage is taken into consideration: overvoltages are neglected since it is difficult to estimate real electrolysis power because of the lack of experimental data for high pressure water electrolysis. Choi et al. [18] consider the cell voltage to be expressed as the sum of the open-circuit voltage and of the overvoltages; the losses taken into consideration are the activation ones (calculated using the Butler–Volmer equation both at the anode and at the cathode), the resistance of the membrane and the interfacial resistance between the electrodes and the membrane. Diffusion overvoltages are neglected since it is assumed that no mass transport limitations exist. Marr and Li [3] develop an electrochemical model referring to PEM fuel cells. The approach used in modelling the Ohmic losses of the bipolar plates has been used by us as starting point for developing the model for high pressure water electrolysis. Bernardi and Verbrugge [4] develop a model for gas diffusion through a polymer electrolyte which is useful for obtaining a relationship between the membrane conductivity and its Hþ ions content. Avalence Llc. [12] reports of an under-development high pressure electrolyser capable of producing hydrogen at pressure up to 34 MPa. Jannsen et al. [7] report in the International Journal of Hydrogen Energy of tests conducted on a 12-MPa alkaline electrolyser prototype, dealing in particular with the safety aspect, which is of primary importance because of the presence of reactive gases and electrolyte at high pressure.

3.

DG E¼ 2F Since the reaction taking place is: 1 H2 O/H2 þ O2 2

its Gibbs free energy change in standard conditions can be evaluated as: 1 DG0 ¼ G0f;products  G0f;reactants ¼ G0f;H2 þ G0f;O2  G0f;H2 O 2

(3)

Since non-standard pressure and temperature conditions are possible, the following relation has been used to apply the pressure correction: pH2 pO1=2 2 DG ¼ DG þ RTcell ln pH2 O

(4)

where DG* is the Gibbs free energy change at any temperature but standard pressure. It can be calculated as follows: DG ¼ DH  Tcell DS

(5)

and therefore, considering that hydrogen is developed at the cathode whereas oxygen and water are present at the anode:    1 DG ¼ HH2 ðTcat Þ þ HO2 ðTan Þ  HH2 O ðTan Þ  Tcell SH2 ðTcat ; P0 Þ 2  1 þ SO2 ðTan ; P0 Þ  SH2 O ðTan ; P0 Þ 2 (6) Enthalpy and entropy have been evaluated in dependence of temperature and pressure using the following experimental data fitting expressions [5]: 4 2 4 HðTÞ ¼ aj T þ bj T5=4 þ cj T3=2 þ dj T7=4 5 3 7

(7)

4 SðT; PÞ ¼ aj ln T þ 4bj T1=4 þ 2cj T1=2 þ dj T3=4  R ln P 3

(8)

They are valid in a temperature range between 300 and 4000 K, and the coefficients have the values shown in Table 1. The results are shown in Fig. 1, reporting the open-circuit voltage depending on the temperature and pressure conditions.

Theoretical model 3.2.

The developed theoretical model aims at expressing the relationship between the electrolytic cell voltage and cell current. As widely known the real cell voltage in an electrolytic cell is higher than the ideal open-circuit voltage and can be expressed as: V ¼ E þ hact þ hohm þ hdiff

Activation overvoltage

The current density at the electrode/electrolyte interface can be expressed for each electrode thanks to the Butler–Volmer equation, which takes into account the kinetics of the charge transfer reaction [21,6]:

(1)

Each of these terms is analysed in the following.

3.1.

(2)

Table 1 – Values of the coefficients for equations (7) and (8).

Open-circuit voltage

When the electrochemical cell operates in reversible conditions, that is, in open-circuit conditions, its voltage can be expressed as:

j¼1 j¼2 j¼3

Substance

aj

bj

cj

dj

Water Hydrogen Oxygen

180 79.5 10.3

85.4 26.3 5.4

15.6 4.23 0.18

0.858 0.197 0

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Polarisation curve. Parameter: Anode exchange current density

Cell voltage [V]

2.2 2 1.8 1.6 10−7 A/cm2 10−10 A/cm2 10−12 A/cm2

1.4 1.2 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Cell current density [A/cm2] Fig. 1 – Open-circuit voltage as a function of the temperature and pressure conditions.

Fig. 3 – Influence of the anode exchange current density on the whole polarisation curve for 1 cell.

     a1 F a2 F i ¼ i0 exp hact  exp  hact RT RT

(9)

Assuming a1 ¼ a2 [13,6], equation (9) can be easily inverted, yielding: hact ¼

  RT i arcsinh aF 2i0

(10)

i0, an ¼ 107 O 1012 A/cm2 for Pt and Pt–Ir based catalysts, respectively. Literature values for i0, an are also much dispersed in a range between 1013 and 106 A/cm2. It was therefore chosen the value which allowed the best experimental data fitting.

3.3.

Diffusion overvoltage

which can be applied both for the anode and the cathode: hact;an

RTan i arcsinh ¼ aan F 2i0;an

hact;cat ¼

(11)

RTcat i arcsinh acat F 2i0;cat

(12)

where aan ¼ 2 and acat ¼ 0.5. The exchange current densities are, however, unknown parameters, but their determination is very important: in fact, their values have a great influence on the final polarisation curve (shown in the model sensitivity analysis in Figs. 2 and 3). Several values are available in the literature for fuel cells, but very few for electrolysers; Choi et al. [18] suggest for example i0, cat ¼ 103 A/cm2 for Pt based catalysts, and

Polarisation curve. Parameter: Cathode exchange current density

Cell voltage [V]

2.2 2 1.8 1.6 10−1 A/cm2 10−3 A/cm2 10−5 A/cm2

1.4 1.2 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Cell current density [A/cm2] Fig. 2 – Influence of the cathode exchange current density on the whole polarisation curve for 1 cell.

The diffusion overpotential (or concentration overpotential) takes into consideration the mass transport limitations that can occur especially at high current densities. In fact, in the case of water electrolysis, the electrochemical reaction needs water to be supplied to the reaction site, and hydrogen and oxygen to be removed. Since the reaction is taking place at the membrane–electrode interface, all the mass flows must be transported through the porous electrode: water from the channels to the catalyst layer, hydrogen and oxygen from the reaction sites to the channels. The flow encounters of course a resistance when flowing through the electrode, and this resistance increases with increasing flow: it is clear that some energy is lost in order it to be overcome, and this is the cause of diffusion overvoltages: the cell voltage to be imposed is higher because of the mass transport limitations. The mass flow through the porous electrodes is a diffusion phenomenon, described by Fick’s law since in the case of water electrolysis just two-components mixtures are present (O2/H2O mixture at the anode, and H2/H2O mixture at the cathode). In the case of water electrolysis, it is likely that the biggest influence is due to the products transport limitations: in fact, if H2 and O2 are not removed as fast as they are produced, their concentration in the reaction site increases, slowing the reaction kinetics. The diffusion overvoltage can be estimated with the Nernst equation:     RT RT RT C1 hdiff ¼ V1  V0 ¼ E0 þ ln C1  E0 þ ln C0 ¼ ln zF zF zF C0

(13)

where the ‘‘0’’ condition is a working condition taken as reference.

international journal of hydrogen energy 34 (2009) 1143–1158

Equation (13) can be applied both for the anode and the cathode, yielding: hdiff;an

RTan CO2 ;me ln ¼ 4F CO2 ;me;0

hdiff;cat ¼

RTcat CH2 ;me ln 2F CH2 ;me;0

(14)

(15)

where CO2 ;me and CH2 ;me indicate, respectively, the oxygen and hydrogen concentration at the membrane–electrode interface, which will be determined in the following subsection.

3.4.

Mass flows inside the cell

Fig. 4 shows the mass flows inside the electrolysis cell (expressed in mol/s), where N_ H2 O;in is the molar water inlet flow at the anode. N_ H2 O;out;an is the molar water outlet flow from the anode. N_ H2 O;out;cat is the molar water outlet flow from the cathode. N_ O2 ;prod is the molar oxygen flow produced at the anode. N_ H2 ;prod is the molar hydrogen flow produced at the cathode. N_ H2 O;dd is the molar water flow due to the concentration gradient. In this case the flow from the anode to the cathode prevails. N_ H2 O;eo is the molar water flow from the anode to the cathode, due to the electro-osmotic drag. N_ H2 O;pe is the molar water flow from the cathode to the anode, due to the pressure effect. In fact hydrogen is produced at the cathode at elevated pressure, and therefore a water flow can exist due to this differential pressure across the membrane. N_ H2 O;cons is the molar water flow consumed by the electrochemical reaction and split into hydrogen and oxygen. According to Faraday’s law, the following expressions are valid: I N_ H2 O;cons ¼ 2F I N_ H2 ;prod ¼ 2F I N_ O2 ;prod ¼ 4F Introducing the net water flow through the membrane:

(16) (17) (18)

N_ H2 O;m ¼ N_ H2 O;dd þ N_ H2 O;eo  N_ H2 O;pe

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(19)

the following relations can be obtained from the mass conservation at anodic and cathodic chambers: N_ H2 O;out;an ¼ N_ H2 O;in  N_ H2 O;out;m  N_ H2 O;cons

(20)

N_ H2 O;out;cat ¼ N_ H2 O;m

(21)

The water flows through the membrane are due to three different phenomena and can be evaluated as follows: N_ H2 O;dd : this contribution is due to the fact that there is a water concentration gradient across the polymeric membrane, and therefore a water flow arises, in this particular case prevalently from the anode to the cathode; it can be evaluated by the following relation [2,13,20]:  ADw  CH2 O;me;cat  CH2 O;me;an N_ H2 O;dd ¼ dm

(22)

where Dw is the water diffusion coefficient in the membrane, dm the membrane thickness and CH2 O;me;cat , CH2 O;me;an represent the water concentrations at the two sides of the membrane. N_ H2 O;eo : the water electro-osmotic drag arises since the Hþ ions, while conducted through the membrane from the anode to the cathode, drag some water molecules with themselves; the amount of this phenomenon is evaluated through the electro-osmotic drag coefficient nd ½molH2 O =molHþ  and the molar flow can be expressed as [2,13,19]: I N_ H2 O;eo ¼ nd F

(23)

N_ H2 O;pe : the water flow due to the pressure gradient across the membrane is the only one going from the cathode to the anode; it can be evaluated thanks to Darcy’s law [14]: N_ H2 O;pe ¼ Kdarcy

ArH2 O mH2 O Mm;H2 O

(24)

The evaluation of the water flows through the membrane depends on the values adopted for the coefficients. Values frequently adopted in the literature are:

nd ¼ 0.27 Dw ¼ 1.28  1010 Kdarcy ¼ 1.58  1018

molH2 O =molHþ m2/s m2

[19,16] [20,16] [4]

As regarding nd, a values of 7 has been used since it was experimentally evident that a huge amount of water was transported to the cathodic side of the membrane, and therefore that the electro-osmotic drag was very important. Solving equation (19) with respect to N_ H2 O;dd and substituting it into equation (22) yields:  ADw  N_ H2 O;m  N_ H2 O;eo þ N_ H2 O;pe ¼ CH2 O;me;cat  CH2 O;me;an dm Fig. 4 – Mass flows inside the cell.

(25)

Water concentration at both sides of the membrane can be expressed as a function of water concentration in the

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electrode channel. In fact, according to Fick’s law of diffusion and considering the conventions shown in Fig. 5, the following equations apply: n_ H2 O;an

CH O;ch;an  CH2 O;me;an ¼ Deff;an 2 de;an

n_ H2 O;cat ¼ Deff;cat

(26)

de;an n_ H2 O;an Deff;an

(28)

de;cat n_ H2 O;cat Deff;cat

(29)

where Deff, an and Deff, cat are, respectively, the O2/H2O and the H2/H2O effective binary diffusion coefficients [2,13]. They can be calculated by applying the porosity correction to the diffusion coefficients; here the correction suggested by Ref. [17] is used, since it is widely cited in the literature [13,16]:   3  3p a Deff;AB ¼ DAB 3, 1  3p

(30)

where 3 is the porosity of the electrodes, which is taken to be 0.3 [13,16,8]. 3p is the percolation threshold, which is taken to be 0.11 [13,16,9]. a is an empirical coefficient, whose value is 0.785 [13,16,9]. The binary diffusion coefficient for any given mixture of the two substances A and B can be estimated as follows [2, 13]:

PDAB

!b  1=2  1=3 T 1 1 ¼ a pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðTc;A Tc;B Þ5=12 þ pcA pcB Mm;A Mm;B Tc;A Tc;B (31)

where P is the pressure, to be measured in [atm]. T is the temperature [K]. DAB is the binary diffusion coefficient of the mixture [cm2/s]. a and b are dimensionless empirical coefficients (see Table 2). Tc, pc and Mm are the critical temperature, critical pressure and molar mass, respectively (see Table 3). Substituting equations (28) and (29) into equation (25) one obtains:

CH2,me nH2

ð32Þ

Considering that in the channel water is present in liquid form, the following applies: CH2 O;ch;an ¼

rH2 O ðTan Þ Mm;H2 O

CH2 O;ch;cat ¼

rH2 O ðTcat Þ Mm;H2 O

(33)

Moreover, the water going through the anode is the water consumed by the reaction, plus the net water transported towards the other side of the membrane, and therefore: n_ H2 O;an ¼

N_ H2 O;m þ N_ H2 O;cons A

(34)

whereas at the cathode side one has: n_ H2 O;cat ¼

N_ H2 O;m A

(35)

The substitution of equations (33)–(35) into equation (32) allows the latter to be solved with respect to N_ H2 O;m , yielding1: N_ H2 O;m;A N_ H2 O;m ¼ N_ H2 O;m;B

(36)

where  ADw rH2 O ðTcat Þ  rH2 O ðTan Þ N_ H2 O;m;A ¼ N_ H2 O;eo  N_ H2 O;pe þ dm Mm;H2 O  _ de;an NH2 O;cons þ Deff;an A   Dw de;cat de;an þ N_ H2 O;m;B ¼ 1  dm Deff;cat Deff;an

n_ H2 O;an ¼

N_ H2 O;m þ N_ H2 O;cons N_ H2 O;in  N_ H2 O;out;an ¼ A A

n_ H2 O;cat ¼

N_ H2 O;m N_ H2 O;out;cat ¼ A A

CH2,ch

nH2O,cat CH2O,ch,an

3.640  104 2.334

 ADw de;cat n_ H2 O;cat CH2 O;ch;cat þ N_ H2 O;m  N_ H2 O;eo þ N_ H2 O;pe ¼ dm Deff;cat  de;an n_ H2 O;an CH2 O;ch;an þ Deff;an

CO2,me

nO2

2.745  104 1.823

Once the net water flow through the membrane is known, all the other flows can be calculated using the shown equations. In particular:

Membrane

CO2,ch

Pairs of H2O and a nonpolar gas

(27)

and therefore:

CH2 O;me;cat ¼ CH2 O;ch;cat þ

Pairs of two nonpolar gases a b

CH2 O;me;cat  CH2 O;ch;cat de;cat

CH2 O;me;an ¼ CH2 O;ch;an 

Table 2 – Dimensionless coefficients for use in equation (31).

nH2O,an CH2O,me,cat CH2O,ch,cat n_ H2 ¼

CH2O,me,an Anode

N_ H2 ;prod I ¼ A 2FA

Cathode

Fig. 5 – Species concentration inside the cell. The molar flows per area unit through the electrodes are introduced and considered positive as shown in the figure.

The terms N_ H2 O;m;A and N_ H2 O;m;B were introduced just for typographical reasons. 1

international journal of hydrogen energy 34 (2009) 1143–1158

Table 3 – Critical temperature, critical pressure and molar mass of H2, O2 and H2O (values from Ref. [13]).

Tc [atm] pc [K] Mm [g/mol]

n_ O2 ¼

H2

O2

H2O

12.8 33.3 2

49.7 154.4 32

218.3 647.3 18

The molar flows per unit area through the electrodes allow to calculate the concentrations and the partial pressures needed to compute equations (4), (14) and (15). In fact [13,14]: n_ H2 n_ H2 O;cat yH2 O;ch;cat ¼ n_ H2 þ n_ H2 O;cat n_ H2 þ n_ H2 O;cat n_ O2 n_ H2 O;an ¼ yH2 O;ch;an ¼ n_ O2 þ n_ H2 O;an n_ H2 þ n_ H2 O;an

(37)

Once the molar fraction of each species in the channels is known, it is straightforward to calculate the concentrations in the channels: rH O ðTcat Þ Pcat yH2 ;ch CH2 O;ch;cat ¼ 2 RTcat Mm;H2 O rH O ðTan Þ Pan yO2 ;ch ¼ CH2 O;ch;an ¼ 2 RTan Mm;H2 O

CH2 ;ch ¼ CO2 ;ch

(38)

and then, by applying once again Fick’s law, at the membrane– electrode interface:

(43)

Each of the two terms hohm, m and hohm, e will be calculated in the following subsections.

3.5.1.

yH2 ;ch ¼ yO2 ;ch

the stack equivalent resistance can be calculated as the sum of the resistances of each cell, provided that the resistance of the external wires can be neglected. The cell is in its turn made up of the series of the electrodes, the plates and the membrane, and the Ohmic resistance opposed by each of these elements has to be evaluated, although the resistance due to the membrane is usually predominant [21]. The voltage drop due to the membrane can be separated from that due to electrodes and plates as follows:   hohm ¼ Rcell I ¼ Req;an þ Rmem þ Req;cat I   ¼ Rmem I þ Req;an þ Req;cat I ¼ hohm;m þ hohm;e

N_ O2 ;prod I ¼ A 4FA

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Electrodes and plates

The Ohmic resistance of electrodes and bipolar plates can be calculated as: [ Rohm ¼ r A

(44)

where r is the material resistivity [U m], [ is the length of the electrons path and A is the conductor cross section. According to Ref. [3], electrode and plate can be modeled as a network of Ohmic resistors; the result of this approach is shown in Fig. 6. The assumption in a 0D model of polarisation is that the current density per unity of area is uniform at the interface between each electrode and the membrane. The material

de;cat de;cat n_ H CH2 O;me;cat ¼ CH2 O;ch;cat þ n_ H O;cat Deff;cat 2 Deff;cat 2 de;an de;cat n_ O CH2 O;me;an ¼ CH2 O;ch;an þ n_ H O;an ¼ CO2 ;ch þ Deff;an 2 Deff;an 2

CH2 ;me ¼ CH2 ;ch þ CO2 ;me

(39) Then the molar fractions at the membrane–electrode interface can be calculated from the concentrations: RTcat CH2 ;me Pcat RTcat ¼ CO2 ;me Pcat

CH2 O;me;cat CH2 O;me;cat þ CH2 ;me CH2 O;me;an ¼ CH2 O;me;an þ CO2 ;me

yH2 ;me ¼

yH2 O;me;cat ¼

yO2 ;me

yH2 O;me;an

(40)

and the partial pressures, of course, are: pH2 ;me ¼ yH2 ;me Pcat pO2 ;me ¼ yO2 ;me Pan pH2 O;me;an ¼ yH2 O;me;an Pan

(41)

All the quantities needed to compute expressions (4), (14) and (15) are available: it is important to stress that the partial pressure of water was calculated at the anode and not at the cathode since water at the anodic side of the cell is that involved in the electrochemical process.

3.5.

Ohmic overvoltage

The Ohmic overpotential across each cell can be expressed as: hohm ¼ Rcell I

(42)

where Rcell is the Ohmic resistance of each cell inside the stack and I is the stack current. Being the cells connected in series,

Fig. 6 – Model for the calculation of the Ohmic resistance of the electrode and of the plate.

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international journal of hydrogen energy 34 (2009) 1143–1158

constituting the electrode and the plate can therefore be imagined as made up of different separate conductors, each of them opposing a certain resistance to the electrons flow. In this case the electrode material between two adjacent channels has been divided into two parts, each of them wide one half of the channel support width. On the contrary, the material in front of a channel has been considered as a whole. Therefore, the equivalent resistance (for the anode and cathode case) is: RES;an

de;an ¼ re;an w s;an L 2

RES;cat

de;cat ¼ re;cat w s;cat L 2

RED REC

RED

(45)

de;an de;cat REC;cat ¼ re;cat wc;an L wc;cat L

(46)

for the material in front of the channel. re, an and re, cat are, respectively, the anode and cathode material resistivity, wc, an and wc, cat the channel width, ws, an and ws, cat the channel support width, de, an and de, cat the anode and cathode thickness. L is the MEA length, in direction orthogonal to the section in the figure. Considering that the electrons coming from the electrode must go through the plate, it is clear that some of them must go around the channel, since they cannot travel straight on like the others. Therefore for these electrons, the additional resistances RED have been added; taking into account the electrons path average length, they can be calculated as follows: wc;an RED;an ¼ re;an 4 de;an L

RED;cat ¼ re;cat

wc;cat 4 de;cat L

(47)

because the electrons are in this case travelling in vertical direction (therefore length and width are exchanged in respect with before, when they were travelling horizontally). Once they are in the plate, the electrons firstly travel through the channel support and then in the back part. Each support has been considered as divided in two parts, each opposing a resistance calculated as follows: RPS;an

hc;an ¼ rpl;an w s;an L 2

RPS;cat

hc;cat ¼ rpl;cat w s;cat L 2

Fig. 7 – Electric structure repeated around each channel of the plate.

Through the series of transformations shown in Fig. 8 this structure can be simplified, thus leading to the calculation of the equivalent resistance of each channel, both for the anode and for the cathode: Req, ch, an and Req, ch, cat. Therefore, repeating the transformations for both the electrodes, it is possible to calculate the equivalent resistance of each channel, for the anode and for the cathode: Req;ch;an ¼ RT;an ==ðRB;an ==RS;an þ RR;an ==RPS;an Þ

(50)

Req;ch;cat ¼ RT;cat ==ðRB;cat ==RT þ RR;cat ==RPS;cat Þ

(51)

RES RPS

R1 = RA

R1

RA = 2 · REC + RED RPS RES

RB = RES // RA RPS R1

(48)

RPR;an

RPR;cat

RB = RES //RA

RPS RB = RES // RA

RT RR

RS

hp;cat ¼ rpl;cat A

2 2 · REC · RED + RED REC

RA

where rpl, an and rpl, cat are the electrode resistivities, hc, an and hc, cat the channel height. The back part of the plate has instead been considered as a whole because it is homogeneous; its resistance therefore is: hp;an ¼ rpl;an A

RPS

RES

for the material in front of the support channel, and: REC;an ¼ re;an

RPS

RES

(49)

All the resistances in the equivalent network shown in Fig. 6 are therefore known from material and geometric data; in order to calculate the resistance of the whole it is now necessary to perform some transformations of the electric network in other equivalent networks. First of all, it is clear that each channel involves the common structure shown in Fig. 7, which is therefore repeated nch, an times in the anode and nch, cat times in the cathode, with nch, an and nch, cat the number of channels in the anode and cathode plate, respectively.

RR =

RB RPS + RB R1 + RPSR1 RB

RS =

RB RPS + RB R1 + RPSR1 RPS

RT =

RB RPS + RB R1 + RPSR1 R1

RPS

RB

RT

Req,ch = RT // (RB //R

RB // RS

RR // RPS Fig. 8 – Series of transformations.

S

+ RR //R PS)

international journal of hydrogen energy 34 (2009) 1143–1158

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Once the equivalent resistance of each channel is known, the resistance of the whole electrode and plate assembly can be calculated according to Fig. 9, which shows as an example a plate with 2 channels, equivalent to that shown in Fig. 6. Considering that all the resistors of the channels are in parallel, and that in general the channels are nch, an for the anode and nch, cat for the cathode, the overall resistances for each cell are: Req;an ¼

RES;an þ RPS;an Req;ch;an == þ RPR;an 2 nch;an

(52)

Req;cat ¼

RES;cat þ RPS;cat Req;ch;cat == þ RPR;cat 2 nch;cat

(53)

Fig. 10 – Sketch of the circular MEA with its variable-length channels, and of the equivalent rectangular MEA with constant-length channels.

and therefore the voltage drop across each cell due to electrodes and plates is:   hohm;e ¼ Req;an þ Req;cat I

(54)

Up to now a rectangular-shaped membrane–electrodeassembly (MEA) has been considered, with length L and width W (and area A ¼ WL) since it was easy to calculate its equivalent resistance. However, the considered electrolyser has a circular MEA, and this has to be taken into consideration. The chosen approach was to introduce an equivalent rectangular MEA, in which each channel has a length equal to the average length of the channels of the circular MEA (see Fig. 10). To calculate the length of each channel and of each support of the circular MEA, the length in the middle of them is taken into consideration. It can be easily calculated from elementary geometry, provided that the distance of the middle line of the channel or of the support from the circumference centre is known. Considering the frontal view of the channels shown in Fig. 11, where the distance of the first channel and of the first support are indicated as yc, 1 and ys, 1, respectively, it is clear that the distance of the middle line of the j-th channel from the centre can be calculated as:

RES

  1 nch nch yj ¼ j  ðwc þ ws Þ with j ¼  ; .; 2; 1; 1; 2; .; 2 2 2

(55)

whereas the distance of the j-th support from the centre is: yj ¼ jðwc þ ws Þ

nch nch with j ¼  ; .; 2; 1; 0; 1; 2; .; 2 2

(56)

Given the circumference radius r, it is obvious that the length of any chord distant yj from the centre is:

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi L y ¼ yj ¼ 2 r2  y2j

(57)

It is therefore straightforward to calculate the average length of the channels:

Lavg;ch

1 X 2 X ¼ Lj ¼ nch cjs0 nch cjs0

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi  2 1 2 2 r  j ðwc þ ws Þ 2

(58)

and that of the supports:

RPS

Req,ch

RPR Req,ch

RES

RPS

Fig. 9 – Simplified circuit for the calculation of the ohmic resistance of the electrode and plate assembly.

Fig. 11 – Frontal view of the channels: the middle support is numbered as zero, while the other supports (painted in the drawing) are numbered with positive and negative numbers. The channels (empty in the drawing) are also numbered but the number zero is excluded. The width of each channel is indicated as wc, while the width of the supports is referred to as ws.

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international journal of hydrogen energy 34 (2009) 1143–1158

Lavg;supp ¼

1 X 2 X Lj ¼ nch þ 1 cj nch þ 1 cj

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2  j2 ðwc þ ws Þ2

(59)

Voltage drop across the membrane

0.35

Simplified expr. Complete expr.

0.3

3.5.2.

Membrane

The ohmic resistance of the membrane, due to the resistance encountered by the ions to flow through it, is greater than that of the electronic conductors. An equation correlating the electric potential gradient across the membrane with the cell current density can be found in Ref. [4]2: it considers both the voltage drop due to ohmic losses and to the diffusion potential. This equation can be simplified in this case since a zero-dimensional approach has been adopted; therefore its integration over the membrane thickness yields:

hohm;m ¼ dm

I Asm

þ

FðPcat Pan ÞKdarcy CHþ s m m H O dm 2

1þ

F2 Ktexte C2 þ

(60)

H

sm mH

2O

where sm is the membrane conductivity. Choi et al. [18] use instead the expression: hohm;m ¼ dm

I Asm

(61)

which can be obtained from equation (60) by neglecting the second term in the numerator. Fig. 12 compares the two expressions of the voltage drop across the membrane as a function of the cell current: it is clear that the difference is very little, and therefore the simpler expression (61) was chosen, also because it shows no voltage drop for zero current. The membrane conductivity must still be determined. Bernardi and Verbrugge [4] suggest the expression: 2

sm ¼

F CHþ DHþ RTcell

(62)

since in the membrane the only mobile ions are the hydrogen ions, whose concentration and diffusivity are indicated as CHþ and DHþ , respectively. Another conductivity expression, which takes into account also the membrane hydratation, is reported in Ref. [15]:

2

Together with some values for the involved quantities.

Voltage [V]

0.25 0.2 0.15 0.1 0.05 0

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Cell current density [A/cm2] Fig. 12 – Comparison of two expressions of the voltage drop across the membrane as a function of the cell current. ‘‘Simplified expression’’ refers to equation (61), while ‘‘Complete expression’’ refers to equation (60).

   1 1 sm ¼ ð0:005139l  0:00326Þexp 1268  303 Tcell

(63)

where l is the degree of humidification of the membrane, expressed as the molH2 O =molSO3 ratio. While in fuel cells it is quite important to evaluate l since the membrane hydratation can vary in a large interval, in the case of this PEM electrolyser the whole membrane can be considered fully hydrated, since water is present in huge quantities in the anodic chambers (and also on the cathodic side due to transport phenomena). Usually in such cases l is assumed in the range 14–21 [14], but we assumed values up to l ¼ 25. Fig. 13 shows the trend of both expressions as a function of l at different temperatures (of course expression (62) does not vary with l). It is clear that in the assumed values of l the two expressions yield very similar results; since l is not expected to vary during normal operation, expression (62) was used, also because expression (63) was obtained by fitting Nafion 117based experimental data, and therefore it could bring to less accurate results because Nafion 110 is in this case instead used. The sensitivity of the whole polarisation model to the parameters used in equations (62) was studied: the results are shown in Figs. 14 and 15. Both concentration CHþ and

0.22

Membrane conductivity

0.2 0.18

σm [S/cm]

which can then be used in equations (45) O (48). However, only some information about geometry and materials is available. From sensitivity analysis it is clear that just the supports width has some influence, whereas the variations due to the other geometric parameters are negligible. This is very important because it assures that the uncertainty in the knowledge of many geometric data does not introduce severe errors in the model. The influence of the electrodes resistivity is negligible as well, while that of the plates has some importance: Marr and Li [3] suggest a value of 60  106 U m for plates, and about 130  106 U m for electrodes (taking into account porosity correction). These studies were, however, carried out considering PEM fuel cell: in the case of this high pressure PEM electrolyser, the support plates and the electrodes are more conductive, due to the internal structure. A value of 50  106 U m was therefore used for the electronic conductors inside the cell.

0.16 0.14 0.12

Expr.1 50°C Expr.1 60°C Expr.1 70°C Expr.2 50°C Expr.2 60°C Expr.2 70°C

0.1 0.08 0.06 10

15

20

25

λ [molH2O/molSO−3 ] Fig. 13 – Comparison of the expressions (62) and (63) for the Nafion membrane conductivity.

international journal of hydrogen energy 34 (2009) 1143–1158

Polarisation curve. Parameter: H+ ions concentration in the Nafion membrane

Cell voltage [V]

2.2 2 1.8 1.6

1000 mol/m3 1200 mol/m3 1600 mol/m3 2000 mol/m3

1.4 1.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Cell current density [A/cm2] Fig. 14 – Influence on the cell polarisation of the HD ions concentration in the Nafion membrane.

diffusivity DHþ of the Hþ ions have a significant influence on the polarisation curve, so their values should be carefully chosen. Bernardi and Verbrugge [4] suggest CHþ ¼ 1200 mol/ m3, but the not far value of 1000 mol/m3, suggested by the stack manufacturer, was used. DHþ is instead going to be experimentally estimated.

4.

Experimental

The test bench is made up of two main bodies. One is the process unit, shown in Fig. 16a, which contains the electrolyser stack and the devices and systems needed for operation, such as tanks, filters, pumps; the other is the electrical panel, shown in Fig. 16b, containing the power supply and the control electronics.

4.1.

the safety aspect: in fact, due to the polymeric membrane permeability to hydrogen and oxygen, the outlet gas flows are not pure, but mixtures can exist: a small amount of hydrogen can be present in the oxygen outlet flow, and a small quantity of oxygen can be present in the outlet hydrogen flow. In order safe operation to be assured, the concentrations must always be kept outside the flammability interval. The test bench must therefore measure the concentrations and stop operation in case of potential danger. Moreover, all the working conditions have to be measured in order to avoid damages to the stack, for example due to overload. The test bench is made up of five main subsystems. The demineralised water supply system, which ensures a continuous water flow in the cells anodic chambers, in order to cool the system and to supply the water needed for the electrolysis. In steady state operation the water is cooled by exchange with network water, whereas an electrical heater is provided to be used during the start-up phase. The hydrogen circuit, which collects the water/hydrogen mixture and separates hydrogen from water, so that water can be recirculated and hydrogen used or vented. The nitrogen supply, which can inject nitrogen in each part of the plant, in order to assure that no dangerous gas mixtures are present before start-up. The electrical power supply is mainly made up of the AC/DC converter used to power the stack. It is current-controlled, so that it is possible to set the desired current value through the stack, which is then automatically kept constant. Other converters are also used for supplying the auxiliaries. The control and data acquisition system is based on a PLC which acquires all the information provided by sensors and transducers, and controls the actuators in order to make the controlled parameters assume the desired values. It is also responsible for system safety, having to shut down the plant in case anomalies are detected.

Description of the test bench

The test bench has the task to supply the electrical power and the needed fluids in order to ensure the electrolyser stack operation. It allows the variation of several parameters, and the measurement of many quantities. High attention is due to

Polarisation curve. Parameter: H+ ions diffusivity in the Nafion membrane

2.2

Cell voltage [V]

1153

2

4.2.

The high pressure electrolyser stack

The core of the test bench is the high pressure electrolyser stack, supplied by Giner Electrochemical Systems Llc. Figs. 17 and 18 show the main parts of the stack and the stack installed on the test bench, respectively. The recommended operating conditions are shown in Table 4. It is made up of 12 Polymer Electrolyte Membrane (PEM) cells, connected in series, with an active area of 160 cm2 each. Each cell is constituted by two contiguous sections, the anodic one and the cathodic one, separated by a membrane; on the opposite faces of the membrane the electrodes are deposited, with a suitable catalyst layer in order to reduce overpotential.

1.8

4.3.

1.6

2.0 ⋅ 10−9 m2/s 4.5 ⋅ 10−9 m2/s 6.0 ⋅ 10−9 m2/s 7.5 ⋅ 10−9 m2/s

1.4 1.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Cell current density [A/cm2] Fig. 15 – Influence on the cell polarisation of the HD ions diffusivity in the Nafion membrane.

The test session

The test session aims at defining the stack polarisation curve in different conditions of temperature and pressure, in order to investigate their influence on the cell voltage. Moreover, the cathodic exchange current density i0, cat and the Hþ ions diffusivity in the Nafion membrane, DHþ , have been chosen as the parameters to be estimated, in order to have an idea of their trend for different temperatures and pressures. The

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international journal of hydrogen energy 34 (2009) 1143–1158

Fig. 16 – Picture of the process unit and of the electric panel. (a) Process unit. (b) Electric panel.

choice of the parameters to be experimentally estimated was made according to their influence on the model, as resulting from the sensitivity analysis previously conducted. The tests were conducted at 7 different pressure levels (1 O 7 MPa, with a 1 MPa step) and 3 different temperature levels (40, 48 and 55  C). The pressure influence was investigated with higher accuracy since the test bench allowed a better precision in the pressure control than in the temperature control.

The polarisation curve can be plotted once the stack voltage is known for different values of current, at given conditions of pressure and temperature. The experimental procedure followed in each session begins therefore with the start-up of the test bench: once the water temperature has reached the desired value, the electrolyser is started usually with a 40 A current. The anode and cathode pressures are then adjusted, respectively, through the back-pressure controlling valves. When the desired pressures are reached at both sides, 1. Tie down holes (for installation). 2. Anode electrical connection. 3. Cells. 4. Cathode electrical connection. 5. End plate 6. Anode out: water and oxygen outlet flows. 7. Cathode out: high pressure hydrogen outlet flow. 8. Tie bolts and belleville washers to seal. 9. Anode in: water inlet flow.

Fig. 17 – Picture of the electrolyser stack outside the test bench.

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international journal of hydrogen energy 34 (2009) 1143–1158

system to reach steady state operation and to reduce experimental errors. The current should be made vary between 0 A and 224 A, which is the maximum allowed by the stack; it was chosen to proceed by 8 A steps (corresponding to 0.05 A/cm2) up to 48 A, and then by 16 A steps (corresponding to 0.10 A/cm2). In this way the first part of the curve, which has the greatest slope due to activation losses, could be more precisely defined. However, it was not always possible to measure the voltage at all these currents. First of all, it was not possible to reach 224 A since the voltage should be so high (27 V or higher) that it could result in damages to the stack: the maximum current reached was therefore about 200 A, sometimes 220 A, varying with the conditions (at higher pressure for example the overvoltages are higher, and therefore the DC supply voltage limitation was reached at lower currents). On the other hand, when the cathode operating pressure was very high (7 MPa), it was not always possible to work at currents lower than 10 A (0.0625 A/cm2), since the very low hydrogen production rate caused the process to stop for safety reasons.

5. Fig. 18 – High pressure electrolyser stack installed on the test bench. Anode and cathode connections are visible, together with the temperature sensors.

the valves control the outlet flows in order to keep them as constant as possible. In spite of this, some tuning can be necessary when the current changes. The polarisation curve is then determined by imposing different current reference values, and measuring the stack voltage. Both these data are directly acquired by the test bench software, together with a number of other working quantities of the test bench. The data are acquired with a time interval of 1 s and stored in a csv-format file, which is then processed with a MatLab script. The stack voltage is averaged over a time interval of at least one minute, in order both to allow the

Results and model validation

In order to estimate the desired parameters, it was necessary to fit the electrochemical model with the experimental data. The expressions previously shown lead to the complete polarisation expression: (64)

V ¼ E þ hact;an þ hact;an þ hdiff þ hohm;e þ hohm;m

The previous expression can be also written in the form: V ¼ K1 þ K2 arcsinhðK3 IÞ þ K4 arcsinhðK5 IÞ þ K6 I

(65)

where K1 ¼ E þ hdiff 1 2Ai0;an 1 K5 ¼ 2Ai0;cat K3 ¼

RTan aan RTcat K4 ¼ acat K2 ¼

K6 ¼ Req;an þ Req;cat þ

dm Asm

The parameters K5 and K6 had to be determined from data fitting, in order to estimate i0, cat and DHþ , respectively. Table 4 – Electrolyser stack operating conditions. 50 O 60  C 0 O 3.5 bar 0 O 35 bar >5.5 l/min >1 MU/cm

Maximum H2 production rate Current at max. prod. rate Voltage at max. prod. rate Power at max. prod. rate Recommended stack current Voltage at recomm. current H2 prod. rate at recomm. current

1.1 Nm3/h 224 A (1.4 A/cm2) 25 V 5.6 kW 80 A 22 V (at 6.89 bar) 0.4 Nm3/h

0.5%vol 0.5%vol

Polarisation curves in different conditions 2.4

Cell voltage [V]

Temperature Anode pressure Cathode pressure Water flow Water resistivity at 25  C Maximum H2 in O2 content Maximum O2 in H2 content

2.2 2 1.8 Fitting curve A Model results A Experimental points A Fitting curve B Model results B Experimental points B

1.6 Test A: pcat=10 bar, Tan=55°C

1.4

Test B: pcat=70 bar, Tan=40°C 1.2 0

0.2

0.4

0.6

0.8

1

1.2

Cell current density [A/cm2] Fig. 19 – Polarisation curves in different conditions.

1.4

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international journal of hydrogen energy 34 (2009) 1143–1158

Dependence of DH+ on pressure at different temperatures DH+ 10-9 [m2/s]

1.6 40°C 48°C 55°C

1.5 1.4 1.3 1.2 1.1 1 0

10

20

30

40

50

60

70

80

Pressure [bar] Dependence of DH+ on temperature at different pressures DH+ 10-9 [m2/s]

1.6 20 bar

1.5

30 bar

40 bar

42

44

50 bar

60 bar

70 bar

46

48

50

1.4 1.3 1.2 1.1 1 38

40

52

54

56

Temperature [°C] Fig. 20 – Influence of temperature and pressure on DHD .

5.1.

Data analysis

the fitting at low current densities were not successful. It was also tried the use of the Tafel equation:

The experimental data have been analysed by interpolating each polarisation curve with the shown expression, and by calculating for each test the values of the parameters to be estimated. Fig. 19 shows two examples of polarisation curve, reporting the experimental points together with the model results and the interpolation curve. The interpolation appears to be very good, except that at low current densities there are sometimes under or overestimation of the voltage values. Some attempts to improve

RT i ln aF i0;cat

(66)

instead of the Butler–Volmer equation for the calculation of the activation overvoltages. This allowed a little better fitting in the initial part of the curve, where the activation polarisation is predominant, but heavily worsened the one at higher currents. The effect of pressure and temperature on the polarisation curve can be stressed by comparing the cell voltage at one

Dependence of i0cat on pressure at different temperatures

0.2

i0cat [A/cm2]

hact ¼

40°C 48°C 55°C

0.15 0.1 0.05 0

0

10

20

30

40

50

60

70

80

Pressure [bar] Dependence of i0cat on temperature at different pressures

i0cat [A/cm2]

0.2 20 bar

30 bar

40 bar

40

42

44

50 bar

60 bar

70 bar

46

48

50

0.15 0.1 0.05 0 38

52

Temperature [°C] Fig. 21 – Influence of temperature and pressure on i0,

cat.

54

56

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Cell voltage [V]

international journal of hydrogen energy 34 (2009) 1143–1158

Influence of temperature at low pressure (tests n. 4,9,13,20)

2.8 2.6 2.4 2.2 2 1.8 1.6 1.4

40°C, 2 MPa 40°C, 1 MPa 55°C, 1 MPa 55°C, 2 MPa 0

0.2

0.4

0.6

0.8

1

1.2

1.4

Cell voltage [V]

Cell current density [A/cm2] Influence of temperature at high pressure (tests n. 7,12,16,19)

2.8 2.6 2.4 2.2 2 1.8 1.6 1.4

40°C, 6 MPa 40°C, 7 MPa 55°C, 7 MPa 55°C, 6 MPa 0

0.2

0.4

0.6

0.8

1

1.2

1.4

Cell current density [A/cm2] Fig. 22 – Influence of temperature on the polarisation curve in low and high pressure conditions.

current value (in this case, i ¼ 1 A/cm2 has been chosen). A temperature increase from 40  C to 55  C causes a 70 mV voltage decrease at low pressure (1 MPa) and a 100 mV voltage decrease at high pressure (7 MPa). A pressure increase from 1 MPa to 7 MPa causes a 130 mV voltage increase at low temperature (40  C) and a 100 mV voltage increase at high temperature (55  C). It is therefore evident the combined effect of pressure and temperature, and in particular that it could be very effective to conduct electrolysis not just at high pressure but at high temperature too, thanks to the beneficial effect of the latter factor.

5.2. Influence of temperature and pressure on the estimated parameters Figs. 20 and 21 show the trend of the estimated parameters with varying temperature and pressure, whereas Figs. 22 and 23 show the influence of temperature and pressure on the polarisation curves.

Influence of pressure (tests n. 4,7,9,12,18,21)

Cell voltage [V]

2.4 2.2 2 1.8 40°C, 1 MPa 40°C, 4 MPa 40°C, 7 MPa 55°C, 1 MPa 55°C, 4 MPa 55°C, 7 MPa

1.6 1.4 1.2 0

0.2

0.4

0.6

0.8

1

1.2

1.4

Cell current density [A/cm2] Fig. 23 – Influence of pressure on the polarisation curve in low and high temperature conditions.

The results can be resumed up as follows. The electrolysis reaction is endothermic and is therefore facilitated by an higher operating temperature: therefore the overall cell voltage is expected to decrease with temperature. As it was expected, the diffusion coefficient of Hþ ions in the Nafion membrane (that is directly related to the membrane conductivity) increases with increasing temperature and decreases with increasing pressure (though in this second case there is sometimes a little increasing trend at low pressures). The first effect reflects into a decrease of the cell voltage (and therefore in the power needed) and was expected since the transport properties of the Nafion membrane are enhanced by a higher temperature. A higher pressure at the cathode is instead expected to cause a voltage increase since it opposes the movement of the Hþ ions from the anode to the cathode, thus making the progress of the reaction more difficult. The cathode exchange current density increases with increasing temperature (causing activation overvoltages to decrease), since the kinetics of the charge transfer reaction at the electrode–electrolyte interface is improved at higher temperature. At the same time, the cathode exchange current density appears first to decrease and then to increase with increasing pressure. This behaviour seems to indicate the presence of two opposite effects, causing a convex shape with a minimum of the parameter. From one part, the high counter-pressure could reduce the kinetics of the charge transfer, but from another part the local concentration of the Hþ ions increases, with a positive effect on the kinetics. We have to better understand this behaviour: further investigation is required. There is an interaction between temperature and pressure; in fact, influence of pressure at high temperature seems lower than at low pressure (Fig. 23), as well as temperature influence seems higher at higher pressures than at low pressures (Fig. 22).

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international journal of hydrogen energy 34 (2009) 1143–1158

Conclusions

This work has deeply analysed the behaviour of a prototype of high pressure Polymer Electrolyte Membrane electrolyser stack. Its performances were studied both from the theoretical and experimental point of view, since a model based on electrochemical equations was developed and then validated by using experimental data. In particular, the dependence on temperature and pressure of the cathodic exchange current density and of the diffusion coefficient of Hþ ions in the Nafion membrane was investigated. As it was expected, both DHþ and i0, cat are strongly dependent on temperature and pressure conditions. In particular, the diffusion coefficient of Hþ ions in the Nafion membrane, directly related to the membrane conductivity and therefore to the cell Ohmic losses, clearly increases with increasing temperature, while the pressure effect is less obvious. The cathode exchange current density increases with increasing temperature due to the improvement of the reaction kinetics. The effect of cathode pressure on the charge transfer kinetics is not monotone and needs further investigation. The joint effect of pressure and temperature urges the development of membranes made up of materials other than the traditional Nafion: this could in fact allow higher operating temperatures, keeping down the pressure negative effects on voltage. Also interesting could be a more detailed study of the water flows through the membrane, in particular a more precise evaluation of the electro-osmotic drag coefficient nd: we are planning this experiment by measuring the net amount of water transported to the cathode (the test bench allows this to be done quite easily) in certain working conditions. Further research should regard the substitution of the analytical 0D model so far used with a numerical model, which could be able to achieve better results, instead of simply using approximate analytical expressions.

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